Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 22, 2024

Find equations with the same solution as $x^2 - 16x - 8 = -7$ .

STEP 1

Assumptions
1. We are given the equation $x^{2} - 16x - 8 = -7$ .
2. We are looking for an equation that has the same solution as the given equation.

STEP 2

To find an equation with the same solution, we need to manipulate the given equation algebraically without changing the solutions.

STEP 3

First, we can simplify the given equation by moving all terms to one side to set the equation equal to zero.
$x^{2} - 16x - 8 + 7 = 0$

STEP 4

Now, combine like terms on the left side of the equation.
$x^{2} - 16x - 1 = 0$

STEP 5

The equation $x^{2} - 16x - 1 = 0$ has the same solutions as the original equation $x^{2} - 16x - 8 = -7$ because we have only added 7 to both sides of the original equation, which does not change the solutions.
The equation with the same solution is $x^{2} - 16x - 1 = 0$ .

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